We establish global regularity for weak solutions to quasilinear divergence form elliptic and parabolic equations over Lipschitz domains with controlled growth conditions on low order terms. The leading coefficients belong to the class of BMO functions with small mean oscillations with respect to x.
Bibliographical noteFunding Information:
We would like to thank Dian K. Palagachev for informing us his recent papers [32, 33], and the anonymous referees for their helpful comments. H. Dong was partially supported by NSF grant number DMS-0800129.
- BMO coefficients
- Boundary value problems
- Quasilinear elliptic and parabolic equations
- Sobolev spaces
ASJC Scopus subject areas
- Applied Mathematics